Tests of hidden variable models by the relaxation of the measurement independence condition

TL;DR

This paper investigates how relaxing the measurement independence assumption in Bell tests affects hidden variable models, finding that increasing hidden variables does not improve their ability to replicate quantum correlations.

Contribution

It analyzes the relationship between the number of hidden variables and the degree of assumption relaxation needed to reproduce singlet state correlations.

Findings

More hidden variables do not enhance the reproduction of quantum correlations.

Relaxing measurement independence can allow hidden variable models to mimic quantum results.

The study clarifies the limits of hidden variable models under relaxed assumptions.

Abstract

Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly relaxed, the probability distribution of the singlet state, for example, can be reproduced by a hidden variable model. Models that deal with the relaxation of some condition above, with more than one hidden variable, have been studied in the literature nowadays. In this work the relation between the number of hidden variables and the degree of relaxation necessary to reproduce the singlet correlations is investigated. For the examples studied, it is shown that the increase of the number of hidden variables does not allow for more efficiency in the reproduction of quantum correlations.